One more time about the uniqueness of Adam and Eve's genome

I’m not sure, but let’s take two scenarios:

  1. 20,000 - 50,000 years ago
  2. 10,000 years ago or less.

My question was prompted by the insistence of several Christian philosophers and theologians that Adam and Eve just had to have some physical trait that distinguished them from people outside the Garden. Even if the main distinctive trait of A&E was, for example, their unique calling as God’s representatives, some people think there had to be some ontological basis for it.

On the other hand we have Joshua’s reminder that scientifically, things are not that simple. You can’t guarantee that any genetic trait of A&E will be passed on to all of their descendants. And this seems to be linked to the notion of A&E likely being genetic ghosts, although I’m not entirely sure of how that linkage works either.

So I’m looking to see how absolute this restriction is, by trying to understand how neutral or beneficial mutations can arise and become fixed. Specifically, I’m looking into the possibility that there could be some sophisticated genetic tinkering that happened to Adam and Eve that “activated” some advantageous trait that propagated to a large portion (but not necessarily all) of their descendants. It could be something subtle - not “consciousness” or “free will” or “intelligence” or language - but perhaps a slightly heightened tendency towards religious belief, or something like that.

By “identify”, I mean in the sense that would we be able to know whether this mutation initially came from 1 specific individual (e.g. “Adam”), or a bunch of individuals in the same place, or a bunch of individuals scattered in different places.